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Utah Sen. Mike Lee endorsed Ted Cruz for president Thursday, making him the first senator to do so

Lee praised Cruz for the promises he has made to protect gun rights, fight Obamacare and uphold other conservative principles

Washington (CNN)Utah Sen. Mike Lee endorsed Ted Cruz for president Thursday, making him the first senator to back the Texas lawmaker, and delivering another blow to Marco Rubio.

Lee praised Cruz for the promises he has made to protect gun rights, fight Obamacare and uphold other conservative principles, in an announcement just hours before CNN's Republican debate.

"Ted has kept those promises and every other promise he has made to the people of Texas," Lee said. "It is with that trust that he's earned that he's going to move forward and unite our party."

The nod from the tea party favorite comes as Republican leaders have grappled with the reality that Cruz, not Rubio, appears best poised to defeat Donald Trump for the Republican nomination. It's also notable because Cruz has alienated many GOP Senate colleagues over his tactics on legislation since entering the chamber in January 2013.

The Texas senator picked up a big endorsement from former rival Carly Fiorina Wednesday, after she said she was "horrified" by Trump. And Sen. Lindsey Graham, a former Republican candidate, is leading the push to rally his colleagues and party leaders to get behind Cruz, based on the senator's lengthy record as a Republican and his strong messaging skills.

But many Republican senators, like North Carolina's Richard Burr, have said they would be open to supporting Trump.

Many establishment Republicans and lawmakers flocked to Rubio, the Florida senator. But his poor performances in recent contests have left them considering either Trump or Cruz -- both of whom have built campaigns as Washington outsiders lambasting the Republican establishment.